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| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2017年01月11日(水)
18:00-19:00 数理科学研究科棟(駒場) 056号室
Lei Fu 氏 (Tsinghua University)
Deformation and rigidity of $\ell$-adic sheaves (English)
Lei Fu 氏 (Tsinghua University)
Deformation and rigidity of $\ell$-adic sheaves (English)
[ 講演概要 ]
Let $X$ be a smooth connected algebraic curve over an algebraically closed field, let $S$ be a finite closed subset in $X$, and let $F_0$ be a lisse $\ell$-torsion sheaf on $X-S$. We study the deformation of $F_0$. The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By studying this rigid analytic space, we prove a conjecture of Katz which says that if a lisse $\overline{Q}_\ell$-sheaf $F$ is irreducible and physically rigid, then it is cohomologically rigid in the sense that $\chi(X,j_*End(F))=2$, where $j:X-S\to X$ is the open immersion.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理，Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
Let $X$ be a smooth connected algebraic curve over an algebraically closed field, let $S$ be a finite closed subset in $X$, and let $F_0$ be a lisse $\ell$-torsion sheaf on $X-S$. We study the deformation of $F_0$. The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By studying this rigid analytic space, we prove a conjecture of Katz which says that if a lisse $\overline{Q}_\ell$-sheaf $F$ is irreducible and physically rigid, then it is cohomologically rigid in the sense that $\chi(X,j_*End(F))=2$, where $j:X-S\to X$ is the open immersion.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理，Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
